Upper bounds for the sum of Laplacian eigenvalues of a graph and Brouwer's conjecture

Consider a simple graph G of order n and size m having Laplacian eigenvalues μ1,μ2,…,μn−1,μn = 0. Let Sk(G) =∑i=1kμ i be the sum of k largest Laplacian eigenvalues of G. Brouwer conjectured that Sk...